The symmetry properties of the rovibronic resonance states (Slonczewski resonances) supported by an upright conical potential are investigated. These symmetry properties lead to a useful correlation between states calculated with and without consideration of the geometrical phase, which can assist in the assignment of those states. The vibronic resonance states of triplet H-3(+) (2(3)A'), which had been studied by us before, have now been assigned to spectroscopic quantum numbers.